As a Catholic, collecting sacramentals such as votive candles, religious pictures, rosaries (which sometimes break), medals, palm branches and other misc. religious items is fairly common. What do you do if you are unsure if they are blessed?
One option, if they are still useable, is to give them away to other people who could use them. If you can’t find any takers there are other options.
The proper disposal of votive candles and other devotionals, if they have been blessed, is to burn or to bury them, most preferably the former in the case of candles. Letting candles burn down entirely, or, if this presents a hazard should the glass candle holders break, burn them by themselves.
It is not a sin to throw away blessed items, but out of proper respect, one should dispose of them in this way. If devotionals have not been blessed, such as some of the holy cards and such that come through the mail, those are simply pictures and can be thrown away.
If you feel uncomfortable throwing them away, you can burn them as well.